### Abstract

Original language | English |
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Title of host publication | Proceedings of the 14th International Symposium on Dynamic Games and Applications (ISDG2010) |

Editors | P. Cardaliaguet, R. Cressman |

Place of Publication | Basel |

Publisher | Birkhauser |

Publication status | Published - 2011 |

### Publication series

Name | Annals of the International Society of Dynamic Games |
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### Cite this

*Proceedings of the 14th International Symposium on Dynamic Games and Applications (ISDG2010)*(Annals of the International Society of Dynamic Games). Basel: Birkhauser.

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*Proceedings of the 14th International Symposium on Dynamic Games and Applications (ISDG2010).*Annals of the International Society of Dynamic Games, Birkhauser, Basel.

**Necessary and sufficient conditions for Pareto optimality in differential games.** / Reddy, P.V.; Engwerda, J.C.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Scientific › peer-review

TY - GEN

T1 - Necessary and sufficient conditions for Pareto optimality in differential games

AU - Reddy, P.V.

AU - Engwerda, J.C.

PY - 2011

Y1 - 2011

N2 - In this article we derive necessary and sufficient conditions for the existence of Pareto optimal solutions for an N player cooperative infinite horizon differential game. Firstly, we write the problem of finding Pareto candidates as solving N constrained optimal control subproblems. We derive some weak conditions which entail one to find all Pareto candidates by solving a weighted sum optimal control problem. We observe that these conditions are related to transversality conditions of the associated subproblems. Furthermore, we derive sufficient conditions under which candidate Pareto solutions are indeed obtained by solving a weighted sum optimal control problem. We consider games defined by nonautonomous and discounted autonomous systems. The obtained results are used to analyze the regular indefinite linear quadratic infinite horizon differential game. For the scalar case we devise an algorithm to find all the Pareto optimal solutions.

AB - In this article we derive necessary and sufficient conditions for the existence of Pareto optimal solutions for an N player cooperative infinite horizon differential game. Firstly, we write the problem of finding Pareto candidates as solving N constrained optimal control subproblems. We derive some weak conditions which entail one to find all Pareto candidates by solving a weighted sum optimal control problem. We observe that these conditions are related to transversality conditions of the associated subproblems. Furthermore, we derive sufficient conditions under which candidate Pareto solutions are indeed obtained by solving a weighted sum optimal control problem. We consider games defined by nonautonomous and discounted autonomous systems. The obtained results are used to analyze the regular indefinite linear quadratic infinite horizon differential game. For the scalar case we devise an algorithm to find all the Pareto optimal solutions.

M3 - Conference contribution

T3 - Annals of the International Society of Dynamic Games

BT - Proceedings of the 14th International Symposium on Dynamic Games and Applications (ISDG2010)

A2 - Cardaliaguet, P.

A2 - Cressman, R.

PB - Birkhauser

CY - Basel

ER -